Transcript Document

School on Digital and Multimedia Communications Using Terrestrial and Satellite Radio Links
The Abdus Salam International Centre for Theoretical Physics ICTP Trieste (Italy) 12 February – 2 March 2001
Antenna Fundamentals (2)
R. Struzak
[email protected]
15 Feb 2001
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please contact the author at
[email protected].
15 Feb 2001
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Summary Slide
•
•
•
•
•
Power Transfer
EM Field
Linear Antenna
Radiation Resistance
Radiation Pattern
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Power Transfer
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Antenna Effective Area
• Measure of the effective absorption area presented
by an antenna to an incident plane wave.
• Depends on the antenna gain and wavelength

2
Ae 
G( ,  ) [m ]
4
2
Aperture efficiency: a = Ae / A
A: physical area of antenna’s aperture, square meters
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Power Transfer in Free Space
PR  PFD  Ae
 GT PT

2
 4r
  GR 


 4 
2
  
 PT GT GR 

 4r 
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2
• : wavelength [m]
• PR: power available at the
receiving antenna
• PT: power delivered to the
transmitting antenna
• GR: gain of the transmitting
antenna in the direction of the
receiving antenna
• GT: gain of the receiving
antenna in the direction of the
transmitting antenna
• Matched polarizations
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Power Transfer: Example 1
• What is the power
received from GEO
satellite
(=0.1m, PT =440 W,
GT=1000)
at Trieste
(distance ~38'000 km,
GR=1)?
• Free space
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  
PR  PT GT GR 
 
 4r 
2
0.1

2
3 
 4.4  10  10  
6 
 4    38  10 
4.4  105  10 2

4.4  1018
 1  1015 W
 150 dB(W)
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2
Power Transfer: Example 2
• What is the power
from a transmitter
(=0.1m, PT=440
mW, GT=1)
received at distance
of 3.8 cm (GR=1)?
• Free space
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  
PR  PT GT GR 
 
 4r 
2
0.1


 4.4  101  1  1  
2 
4



3
.
8

10


4.4  103

4.4  108
 105 W
 50 dB(W)
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2
EM Field
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EM Field of Linear Current Element
Er
z
E
OP

dz
r
E
y



 
E  Er  E  E
 


H  H r  H  H
2
E 
Er  E  E
H 
H r  H  H 
2
2
2
2
2
x
dz: electric current element (short electrical dipole)
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EM Field of Current Element
E  jAFF  jQ  C (sin  )e
 j r
Er  2 AQ  C (cos )e  jr
jA
FF  Q (sin )e  jr
H 
120
E  H r  H   0

2

A  30 2 Idz
1
FF 
r
1
Q
( r ) 2
1
C
( r )3
Idz: “moment of linear current element”
Johnson & Jasik: Antenna Engineering Handbook; T. Dvorak: Basics of Radiation Measurements, EMC Zurich 1991; J. Dunlop, D. Smith Telecommunications Engineering1995, p. 216
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Field Components
1000
Relative fieldstrength
C
100
Q
10
FF
1
FF
0.1
Q
0.01
C
0.001
0.1
1
10
Relative distance
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Field Impedance
100
Short dipole
Z / 377
10
1
0.1
Small loop
0.01
0.01
0.1
1
10
Distance / (lambda/ 2Pi)
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Field
impedance
Z = E/H
depends
on the
antenna
type and
on
distance
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Far-Field, Near-Field
•
Near-field region:
–
–
•
Angular distribution of energy depends on
distance from the antenna;
Reactive field components dominate (L, C)
Far-field region:
–
–
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Angular distribution of energy is independent on
distance;
Radiating field component dominates (R)
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EM Field: Elementary Current Loop
H  120BFF  jQ  C (sin )e
 jr
H r  2 BQ  C (cos )e  jr
E   BFF  Q (sin )e  jr
 3dm
B
4
H   Er  E  0

2
dm  I  LoopArea

dm: “magnetic dipole moment”
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Linear Antenna
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Arbitrary Linear Antenna
60 sin 
 jr ( z )
E  j
I
(
z
)
dze

r
l 2
l 2
• I(z): antenna current
• r: distance
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EM Field of Linear Antennas

  
E  E1  E2  E3  ...
 


H  H1  H 2  H 3  ...
O
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• Summation of vector
components E (or H)
produced by every
antenna element
• In the far-field region,
the vector components
are parallel to each other
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Very Short Antenna
60 sin 
 jr ( z )
dze
)
z
(
I
E  j
l 2
r
l 2
60 sin 
I 0 Le e  jr ( z )
E  j
r
1
Le 
I0
l 2
 I ( z)dz
l 2
• r: distance
• Le: effective length of antenna
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Radiation Resistance
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Self- Impedance
• Transmitting antenna
• Receiving antenna
E
jX: energy stored in near-field
components (E  C, H  L)
Z
Rrad: energy radiated
Z
E = Electromotive
force (open-circuit
voltage) induced by
radio wave
Rlos: energy loss
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Short Antenna Radiation Resistance
• The PFD in the far
field is given by the
Poynting’s vector =
|= E|2/(120)
60I 0 Le
E 
sin 
r
P  
S
• Antenna radiation
resistance =
= 802(Le/)2
120
dS
dS  2r 2 sin d
2
– For other antennas it is much
easier to measure the antenna
impedance.
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E
2

2
2  Le 
P  60   I 0  sin 3 d

0
2
 Le  2
P  80   I 0

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Integration Surface
rsin
rd
dS = 2r2sin()d
r
d

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Radiation Pattern
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Radiation Pattern
• Radiation Intensity = Power per steradian
radiated in a given direction
• Radiation Pattern = Radiation Intensity as
function of the azimuth/ elevation angles
• Generally 3 dimensional
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Short Dipole in Free Space FF
1
H
V
Relative Gain
1
-1
0
0
90
180
270
360
Degrees
Horizontal plane: GVi /GVimax = 1
Vertical plane: GHi /GHimax = |sin |
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Elements of Radiation Pattern
Main lobe
Emax
Sidelobes
Emax /2
Nulls
-180
0
Beamwidth
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180
•
•
•
•
Gain
Beam width
Nulls (positions)
Side-lobe levels
(envelope)
• Front-to-back ratio
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Long Antenna with
Sinusoidal Current Distribution
I ( z )  I 0 cos z
r ( z )  r  z cos
r(z)
z

60 sin 
E  j
I 0 e  jr  cos ze jz cos dz
r
l 2
l 2
r
z cos
60I 0 e  jr
E  j
r
r: distance
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
l
 l

cos
cos


cos



2
 2



sin 


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





Demonstration (Simulation)
LinAntLong
This program simulates radiation pattern of linear
antenna of arbitrary length.
It produces 2D radiation diagrams that show
how the positions and magnitudes of radiation
lobes, and positions of zeros depend on the
antenna length
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Half-wave Dipole (l = /2)
60I 0 e
E  j
r
 jr
 

 cos 2 cos  




sin 




• Radiation resistance = 73.1 ohm
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Half-wave Dipole at Harmonics
Odd harmonics
 L

 L
cos  cos   cos  
 

 
f ( ) 
sin 
L
 (2n  1)
( / 2)
cos(2n  1)( / 2) cos 
f ( ) 
sin 
f ( )  0  (2n  1)( / 2) cos
 (2k  1)( / 2)
1.5
Relative Field-strength
3rd harmonic
1
0.5
cos  (2k  1) /(2n  1); k  0,1,...n.
Fundamental
0
-180
-90
0
90
Elevation angle, degrees
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180
f ( )  max  (2n  1)( / 2) cos  k
cos  2k /(2n  1); k  0,1,...(n  1).
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Antenna Mask (Example 1)
Isotropic gain, dB
0
-5
-10
-15
180
120
60
0
-60
-120
-180
-20
• Typical
relative
directivitymask of
receiving
antenna (Yagi
ant., TV dcm
waves)
Azimith angle, degrees
[CCIR doc. 11/645, 17-Oct 1989)
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Antenna Mask (Example 2)
0
0dB
RR/1998 APS30 Fig.9
Phi0/2
Relative gain (dB)
-10
COPOLAR
-3dB
-20
Phi
-30
-40
CROSSPOLAR
-50
0.1
10
1
100
Phi/Phi0
Reference pattern for co-polar and cross-polar components for satellite
transmitting antennas in Regions 1 and 3 (Broadcasting ~12 GHz)
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